Error analysis of a finite element method for the Willmore flow of graphs | Zendy

Klaus Deckelnick | Zendy; Gerhard Dziuk | Zendy

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Error analysis of a finite element method for the Willmore flow of graphs

Author(s) -

Klaus Deckelnick,

Gerhard Dziuk

Publication year - 2006

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/134

Subject(s) - willmore energy , mathematics , finite element method , a priori and a posteriori , nonlinear system , curvature , flow (mathematics) , mathematical analysis , element (criminal law) , order (exchange) , mean curvature flow , geometry , mean curvature , physics , political science , law , thermodynamics , philosophy , epistemology , quantum mechanics , finance , economics

summary:In this article we discuss numerical scheme for the approximation of the Willmore flow of graphs. The scheme is based on the finite difference method. We improve the scheme we presented in Oberhuber [Obe-2005-2,Obe-2005-1] which is based on combination of the forward and the backward finite differences. The new scheme approximates the Willmore flow by the central differences and as a result it better preserves symmetry of the solution. Since it requires higher regularity of the solution, additional numerical viscosity is necessary in some cases. We also present theorem showing stability of the scheme together with the EOC and several results of the numerical experiments

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